We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values $u=0$ and $\infty$. We study the variation of entanglement and fidelity measures in the ground states as a function of $u$ and specially look for signatures of quantum phase transitions at $u=0$ and $\infty$. The two different entanglement measures used are $S\left(i\right)$ (the single-site von Neumann entropy) and $S\left(i,j\right)$ (the two-body entanglement). At the quantum critical point (QCP) $u=\infty$, the entanglement measure $E$ $\left[=S\left(i\right),S\left(i,j\right)\right]$ vanishes but remains nonzero at the other QCP $u=0$. The first and second derivatives of $E$ with respect to the parameter $u$ and the entanglement length associated with $S\left(i,j\right)$ are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity $F$ and a quantity $\text{ln}\left|D\right|$ related to the second derivative of $F$ and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.

• Received 12 September 2007

DOI:https://doi.org/10.1103/PhysRevA.77.032307